There's more than one way to attach a shade to a lamp, and the UNO fitter is one of the neatest. Instead of a separate harp or holder, a UNO-threaded socket lets the shade thread right onto the socket itself, which simplifies the whole assembly. Knowing whether your lamp is set up for it determines which shades will fit.
The UNO system works by threading. The socket has external threads, and the shade, or a fitter ring on the shade, threads directly onto them, held in place by its own connection to the socket. No harp arching over the bulb, no finial holding a shade on top, just the shade threaded on where the socket is. It's a clean, direct arrangement common on bridge lamps, some floor lamps, and smaller fixtures where a compact shade sits close to the bulb. The appeal is simplicity: fewer parts, a lower profile, and a shade that sits neatly around the bulb. The catch is compatibility. A UNO shade needs a UNO socket, and a lamp built for a harp-and-finial shade won't take a UNO one without changing the setup, so identifying whether your lamp is UNO-threaded is the first question, before you shop for a shade.
Salvager's Note: Check the socket before buying a UNO shade. If the shade threads directly onto a threaded socket, with no harp or top finial, it's a UNO setup. A lamp built for a harp-and-finial shade won't take a UNO shade without conversion.